Abstract
AbstractPluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology.
Funder
H2020 Marie Sklodowska-Curie Actions
Otto-Friedrich-Universität Bamberg
Publisher
Springer Science and Business Media LLC
Reference110 articles.
1. Aczel, P. (1988). N on-well-founded sets (Vol. 14). Center for the Study of Language and Information, Lecture Notes.
2. Anderson, C. A. (1990). Logical analysis and natural language: the problem of multiple analyses. In P. Klein (Ed.), Praktische Logik (pp. 169–179). Vandenhoeck and Ruprecht.
3. Anderson, D. J., & Zalta, E. N. (2004). Frege, Boolos, and logical objects. Journal of Philosophical Logic, 33(1), 1–26. https://doi.org/10.1023/B:LOGI.0000019236.64896.fd.
4. Antos, C., Friedman, S.-D., Honzik, R., & Ternullo, C. (2015). Multiverse conceptions in set theory. Synthese, 192, 2463–2488.
5. Azzouni, J. (1998). On “on what there is.". Pacific Philosophical Quarterly, 79, 1–18.